Smoothing minimally supported frequency wavelets: Part II

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L ² -norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.     

Corner view on the crown domain

In this paper we raise a question about the boundary of the crown domain of a Riemannian symmetric space X. In case X is of Hermitian type we give an affirmative answer.     

AES Depth profiling of semiconducting multilayer structures using an ion beam bevelling technique

An ion beam technique has been developed which allows the preparation of bevels from semiconducting heteroepitaxial structures with smooth surfaces and very flat angles in the order of 0.1°. The bevels are used for AES depth profiling of heterostructures by the line scan technique. Measured and calculated line scans from (Al,Ga)As/GaAs and SiGe/Si test structures are compared to estimate the contributions of the electron escape depth and the ion beam mixing to the depth resolution. Received: 21 August 1996 / Revised: 14 January 1997 / Accepted: 18 January 1997     

Near-infrared absorption spectroscopy of toluene-sulfonate-diacetylene crystals

The near-infrared (NIR) absorption of toluene-sulfonate-diacetylene crystals (PTS) has been investigated during thermal polymerization. It is shown by comparative NIR and IR spectroscopy of deuterated and of protonated PTS at various temperatures, that these absorptions are vibronic in nature. They can be assigned unambiguously to distinct parts of the molecule. No low-lying electronic state has been found.     

Das Grenzflächenverhalten von Carboxymethylcellulose an Baumwolle

Ohne Zusammenfassung     

Cellulose production based on hemicellulose hydrolysate from steam-pretreated willow

The production cost of cellulolytic enzymes is a major contributor to the high cost of ethanol production from lignocellulosics using enzymatic hydrolysis. The aim of the present study was to investigate the cellulolytic enzyme production ofTrichoderma reesei Rut C 30, which is known as a good cellulase secreting micro-organism, using willow as the carbon source. The willow, which is a fast-growing energy crop in Sweden, was impregnated with 1–4% SO₂ and steam-pretreated for 5 min at 206°C. The pretreated willow was washed and the wash water, which contains several soluble sugars from the hemicellulose, was supplemented with fibrous pretreated willow and used for enzyme production. In addition to sugars, the liquid contains degradation products such as acetic acid, furfural, and 5-hydroxy-methylfurfural, which are inhibitory for microorganisms. The results showed that 50% of the cellulose can be replaced with sugars from the wash water. The highest enzyme activity, 1.79 FPU/mL and yield, 133 FPU/g carbohydrate, was obtained at pH 6.0 using 20 g/L carbon source concentration. At lower pHs, a total lack of growth and enzyme production was observed, which probably could be explained by furfural inhibition.     

Structural dependence of non-linear optical properties of 4-Dimethylamino-3-cyanobiphenyl

 4-Dimethylamino-3-cyanobiphenyl (4-DMA-3-CB) was characterized with respect to linear and nonlinear optical properties in a crystal as well as in solution. The crystal structure was studied dependent on the crystallization conditions. It is shown that the crystal structure exhibiting NLO-activity can completely be solved by a combination of electron diffraction and computer modeling. There are four molecules per unit cell in the space group Pna2₁ with dimensions a=10.28 Å, b=22.64 Å, c=5.27 Å. From this model structure the values and orientation of the dipole μ and static second order polarizability β can be calculated. Their relevance to the values obtained by a combination of polarization dependent measurements of Electric Field Induced Second Harmonic Generation (EFISH) and Hyper-Rayleigh-Scattering (HRS) in solution are discussed. The molecular second order polarizability tensor was found to be dominated by one single component. The orientations of the dipole and the vectorial parts of the second order polarizability delivered by the semiempirical calculations are in good agreement with the results of the EFISH and HRS-measurements and allow a deeper insight into the nonlinear optical properties of the crystal. Received: 15 April 1996 Accepted: 21 June 1996     

Two 3D supramolecular polymers constructed from an amino acid and a high-nuclear Ln6Cu24 cluster node

The first successful attempt to construct 3D supramolecular frameworks with high-nuclear 3d-4f heterometallic clusters as a node is reported. The self-assembly of Ln3+, Cu2+ and amino acid in solution leads to the formation of two polymers, 35-nuclear complex [Sm6Cu29] 1 with a primitive cubic net-like structure and 36-nuclear complex [Nd6Cu30] 2 with a face-centred cubic network type structure. Glycine and L-proline, respectively, were used as ligands. It should be noted that 2 has a chiral framework. X-ray structure analyses show that 1 crystallizes in the triclinic P1 space group (a=19.6451(8), b=20.4682(8), c=20.7046(8) A, alpha=89.453(1), beta=66.290(1), gamma=68.572(1) degrees, V=7003.0(5) A3 and Z=1) and 2 belongs to the cubic P2(1)3 space group (a=b=c=32.4341(3) A, V=34 119.7(5) A3 and Z=4). Both complexes utilize Ln6Cu24 octahedral clusters as nodes and trans-Cu(amino acid)2 groups as bridges. Electrical conductivity measurements reveal that both polymers behave as semiconductors.     

Matched/Mismatched interaction of a cyclic hexapeptide with ion pairs containing chiral cations and chiral anions

The binding of a chiral quaternary ammonium ion to a cyclopeptide containing aromatic amino acid subunits is affected not only by the configuration of the cation but also by the configuration of the chiral counterion. Analysis of the binding equilibria shows that complex formation involves interaction of the whole ion pair with the host indicating that steric requirements of the anion influence complex geometry and stability.